Marcelpoil R
Equipe de Reconnaissance des Formes et Microscopie Quantitative, Laboratoire TIM3-IMAG, USR CNRS 690B, Université J. Fourier, CERMO, Grenoble, France.
Anal Cell Pathol. 1993 May;5(3):177-86.
A problem of considerable interest in pattern recognition and data analysis is that of describing the spatial structure of a data set. In the field of biology this could be based on graph construction. Although the minimum spanning tree (MST), contains less information than the Relative Neighbourhood, Gabriel and Delaunay graphs [16], this graph has been frequently used [3-9]. The MST is a subgraph of all the preceding graphs. Two main types of parameters can be derived from a graph. Some of the parameters are derived from the structure of the graph (topological parameters), whereas others are based on the Euclidean metrics of the graph (edge lengths). Since these parameters are used to characterize the spatial structure of data sets, they have to be normalized so that different biological structures may be compared. A model for the normalization of the most common parameters derived from the MST is thus presented here. Two aspects of the problem are considered: (i) omission of the metrics associated dimension of the Euclidean parameters in order to compare biological structures at different scale factors and (ii) elimination of border effects to avoid border artefacts.
在模式识别和数据分析中，一个备受关注的问题是描述数据集的空间结构。在生物学领域，这可以基于图形构建。尽管最小生成树（MST）包含的信息比相对邻域图、加布里埃尔图和德劳内图[16]少，但该图仍被频繁使用[3 - 9]。MST是所有上述图形的子图。可以从一个图形中导出两种主要类型的参数。一些参数源自图形的结构（拓扑参数），而其他参数则基于图形的欧几里得度量（边长）。由于这些参数用于表征数据集的空间结构，因此必须对其进行归一化处理，以便能够比较不同的生物结构。因此，本文提出了一种对从MST导出的最常见参数进行归一化的模型。该问题的两个方面被考虑在内：（i）为了在不同比例因子下比较生物结构而省略欧几里得参数的度量相关维度；（ii）消除边界效应以避免边界伪影。
